Sorry nappyaddict and anyone else suggesting parental leave, they certainly can stop her taking it.
Whatami you are entitled to unpaid parental leave as long as you give the required notice, but your employer can forcibly postpone it for up to 6 months for business reasons, which they may do. They would certainly be able to justify doing it.
I think it's worth asking though. I understand what you are saying about it being busy and providing cover earlier on, but the fact still remains that if they will let you have it off providing you work extra beforehand, then that must mean they can physically manage without you during those two weeks.
Ask about parental leave. You can put in a formal request for it, read here all about it. It's basically intended for this type of thing, so in a way, yes you are as a parent entitled to extra help, but the bottom line is, if it's too busy at work, or too many people are already off at the time you want, your employer can postpone your request as I've said, which wouldn't be much use to you. Try it and see how it goes, otherwise you may have to explore some of the emergency childcare options people have mentioned.
Sorry you are having such a nightmare